


∀ (For All)

by Slant



Category: Flatland - Edwin A. Abbott, Wayward Children Series - Seanan McGuire
Genre: Ambiguous/Open Ending, Bad Maths, Bad set theory, Ia! it [is/is not]! The empty set!, Possible Character Death
Language: English
Status: Completed
Published: 2019-08-03
Updated: 2019-10-29
Packaged: 2020-07-30 08:33:25
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 3
Words: 1,075
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/20094364
Author URL: https://archiveofourown.org/users/Slant/pseuds/Slant
Summary: Even by the high standards of the home for wayward children, the kid who went to Flatland is a weird kid.





	1. Chapter 0: Naïve set theory

"There are worlds of pure mathematics, where every number chimes like crystal as it rolls into reality." Down Among the Sticks and Bones, Seanan McGuire.

Of course, no one welcome in such a place would ever say "chimes like crystal" or indeed, "every number" They are much more likely to say |{x : x ∈ ℚ}| = |{ y : y ∈ crystal chimes}|.  
This may take a little explanation. Sets are groups of elements. In the notation used, sets are written as curly bracers { }, and the "size" of a set, more formally its cardinality or number of elements is written by putting the set in pipes: | { } | , what the set is, that is the elements in the set can be written as a simple list, so a set of 1, 2 and ☺ could be written {1,2,☺}, and would have cardinality 3, thus: |{1,2,☺ }|=3 (the example given earlier, { } is the empty set, so it has cardinality zero, |{}|=0). If you want to define your set members more generally, e.g. the set of letters, you write {x : x ∈ letters}, where ∈ means "is", more-or-less, so the set of x, where x is letters. you don't write {letters}, because {letters} is the set which contains the single element, "letters". The sort of people you meet in worlds of pure mathematics are deeply unhelpful like that. Certain concepts have standard symbols, like ℚ, which represents the rational numbers, and others have to be written out longhand, like "crystal chimes". {x : x ∈ every number} is not well-defined, so if {x : x ∈ every number} = {x : x ∈ ℚ } is undetermined. Rigorously defining what a number is is the sort of thing that people from worlds of pure mathematics care about deeply.

What happens to those who aren't numbers generally doesn't get spoken of.


	2. Chapter 1: group t̶h̶e̶o̶r̶y̶ therapy

"∃ a finite, boundless, orientable plane called Flatland," said Edwina.

"All its citizens are regular geometric shapes, all its buildings face South, and everything glows with a mysterious light. It is ruled over by those with the most sides, one nation under ℵ₀, with peace and harmony ∀."

"You may have already picked up on the issues that the place had, I didn't. I didn't work it out for such a long time."

"It was so sensible. All the rules that were explained to me were logical outcomes of sensible assumptions. And because of that, I thought that any other rules were things that had been proved as a logical outcome of sensible assumptions. They weren't. They were logical outcomes of unexamined assumptions or just something that someone had made up."

"It sets you up for believing explanations, things like that. For trusting, and then when the explanations aren't as good, you still accept them. Unless you were someone who had always argued, but it takes an astonishingly argumentative person to refuse to accept that twice two is four."

"The people there are obsessed with Regularity: that is that each Figure should have its sides and angles equal. So that to know one angle of a person by sight or by Feeling is to know the whole person; no oddities hidden behind a graceful facade, no kinks to be revealed to trusted friends. No respectable public face while you truest self daydreams about fairies or furries. The whole of you to be available for public censure at all times."


	3. Choice Is An Exercise Of Power

**Notes for the Chapter:**

> "The dangers to which we are exposed from our Women must now be manifest to the meanest capacity in Spaceland... - what can it be to run against a Woman, except absolute and immediate destruction?" -Flatland, Edwin A. Abbott

There was a lot of mess in Jack's lab, much of it previously girl. There was also a knife at Edwina's throat, but she was a citizen of Flatland, and the sharpness of her eye/mouth had split the world, so it looked pretty blunt, on the grand scale of things. Also, she had a vorpal eye/mouth, which rather put the horrors of butchery and biology into perspective. Edwina had not been forced to leave her world, which was both a way of thinking and a place, she had chosen to, because it was a way of thinking that was, implicitly, a war crime. She was strange and overly academic, but just because she did think of people and things in much the same way was no reason to treat people as if they were things. Metaphorically, she refused to go there, and in this case her door was the metaphor. 

Abbot was quiet and calm, which was freaking Jill out a bit. She'd seen and perpetrated a lot of horrors on the Moors, and she'd done more since she decided to leave the school, and one thing that was constant was blood, screaming and gibbering. Abbot was looking at her like this was a puzzle that she didn't quite get. Jill pressed her lips together and maintained her show of confidence.

"So are you after some bit of me? How do you intend to cut off my Luminosity?"  
Jill dug the knife into her throat and answered in a gentle sing-song, "I'm sure if I dig around a bit, I'll find it."  
Edwina winced away from the sharp point of pain, {twisting in Jill's grip through higher dimensions, turning her Side towards Jill, and becoming, as all Woman are, a Straight line}/{a meaningless reflex action that achieved nothing as Jill held her in place}. She pushed {up, straining her neck away from the blade, that was after all, sharp enough to draw blood}/{back, the infinitely sharp and near-invisible sub-luminious point of her posterior effortlessly passing into Jill's shoulder}. She had only finite {width, height and depth. By Analogy, she had only finite Duration}/{length, no width or height, so all the force of her could be brought to bear on an infinitesimal volume of meat and bone}.

Christopher and Kade ran in, Jack slightly behind and Nancy drifting in on their heels. They saw {Edwina, bright Arterial blood spurting from her neck, and the pleased expression of someone who has solved a difficult problem on her face}/{Jill, staring at her shoulder in shock and pain as Edwina revolved out of it, first as a two-dimentional figure, Sides slicing effortlessly into Jill's torso and shoulder as she brought her Volume back into Space.}

{The body hit the floor}/{the body hit the floor.}

Jack left for the Moors before the cleaning-up started. She took her sister's {body}/{life} and carried the corpse with her, stepping through bloody portal to a world under a huge, hateful moon where death was, for those with the will and knowledge, little more than a suggestion.


End file.
